I think you are asking some good questions.
One question I would ask is what type of college experience does your daughter want?
UNC is going to be a different college experience than attending a HYP. UNC is a fairly large and homogenous campus (83% of students have to be from NC). It’s your quintessential college town, big school spirit, D1 sports, large Greek presence, with southern hospitality.
HYP will have a much more diverse, international student body with world-class faculty and facilities, huge endowments, and as you mentioned, world wide prestige that can open doors, connections.
Lastly, I would compare and contrast the actual type of 4 year education she will get at UNC vs the ivy. In your situation cost of attendance shouldn’t be the difference maker as you have already saved and ear-marked the money for a private college.
Its great that she has two fabulous options and will thrive whatever choice she makes.